Mind · Reasoning
ConceptualDecomposition
Finding what a concept is made of: locate it, carve it into the dimensions every case it claims needs, test each, search for what is missing, route real cases through it, say how the parts make the whole, and carve again below
Definition
Mechanism
The cognitive act of carving a concept into the differentiated dimensions it needs across every case it claims, rather than the steps of one way of achieving it. A claim frame is stated first: the concept, the purpose of the carve and the range of cases it claims. The concept is then located by climbing SpecializationEdge links to broader kinds, each step naming the genus and the differentia and searching for siblings, and the carve is made on the route back down. Candidate dimensions are generated and each is put to the DecompositionGate tests; a failed or uncertain candidate is reframed, narrowed or kept with its verdict as a labelled alternative in the frontier of the ArchiveServingFrontier. A bounded search then looks for any dimension the accepted set still misses, and a RoutingSanityCheck routes concrete cases through the carve before it is kept. Accepted dimensions are bound to the concept by CompositionEdge links, and the carve declares the Synthesis by which they together make the whole. Each dimension is itself a concept, carved again the same way wherever the MarginalValueRule says further depth pays. A dimension is something every claimed case has. Where cases instead fall into mutually exclusive kinds, the division can be one dimension, a classification axis, but its alternative values are kinds of the concept, linked by SpecializationEdge rather than bound as parts by CompositionEdge. Generic Decompose splits one task into independent subproblems whose solutions combine into the whole; this method carves a concept across every case it claims and adds what that needs: the claim frame, the location among broader kinds, the Necessity and Universality tests, the search for missing dimensions and the routing of real cases.
Invariants
- The claim frame is stated before any candidate is tested.
- The concept is located among broader kinds before it is carved.
- Only candidates that pass the DecompositionGate tests become dimensions.
- The carve declares the Synthesis by which its dimensions make the whole; a concept with no available synthesis is not carved.
- Each accepted dimension can be carved again by the same procedure.
Risks
Failure modes
Procedural carve
the concept is split into the steps of one way of doing it rather than the dimensions it needs, so the carve fits one workflow and not the concept.
Carve in place
the concept is carved as it was stated, without being located among broader kinds, so the carve inherits the stated framing.
Coupled split
two dimensions cannot vary or fail separately; the Independence test can miss overlap that is semantic rather than structural.
Fitted routing
the cases routed through the carve are chosen after it is made, so the check confirms the carve instead of testing it.
Shallow carve
accepted dimensions are not carved in turn where depth would pay, so the result is a list rather than a tree.
Relationships
Builds on
Composes with
Four tests of a decomposition against a stated claim frame: each candidate dimension must pass Necessity, Independence and Universality, and the accepted set must pass Completeness
Combining elements
References
Keep evaluated structures in three layers: an inclusive archive, a selective serving layer and an experimental frontier
Infrastructure
A link stating that a child supplies a differentiated contribution its parent's outward capability requires
Dividing complexity into manageable units
Deepen only while expected improvement plus an exploration credit, divided by incremental cost, exceeds a domain threshold
Test a candidate carve by routing a few concrete tasks through it before it is kept
Infrastructure
A link stating that a child concept is a kind or realization of its parent, forming the route by which problems are located
Used by
Composes with
Decompose quality-constrained production into substance, structure, generation, evaluation, and refinement — five intended low-coupling dimensions a producer must address
Population-based discovery: Generate (parallel diverse solvers) + Reduce (composition-aware selection) behind hard boundaries
Separate prediction (is) from valuation (ought) from principle (override), each behind a typed boundary — the decision record has auditable empirical and normative layers
Decompose empathetic understanding into situation, emotion, intent, response, and boundary — variable-depth recursion tracks the stakes of the interaction
Forecast by ensemble of model-checkpoints from different history horizons, each run through five non-substitutable causal lenses — convergence across time is the signal
Layered epistemic verification (cache → coherence → decomposition → specialists → empirical), with verified claims persisting as content-addressed records — the accretion loop
References
Approach any problem through six dimensions: scope, evidence, constraints, stakeholders, mechanism and dynamics
Extends
Breaking a concept into solver-contract-bound sub-concepts — the move that enables fractal recursion